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GEAR-UP SAT Prep Workshop Math Section

GEAR-UP SAT Prep Workshop Math Section. Claudette Reep September 10, 2011. Problems used in this presentation are from “Cracking the SAT 2009 Edition” published by The Princeton Review. What is the SAT?. A test of “reasoning ability” Not necessarily how “smart” you are 3hrs 45 min

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GEAR-UP SAT Prep Workshop Math Section

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  1. GEAR-UPSAT Prep WorkshopMath Section Claudette Reep September 10, 2011 Problems used in this presentation are from “Cracking the SAT 2009 Edition” published by The Princeton Review

  2. What is the SAT? • A test of “reasoning ability” • Not necessarily how “smart” you are • 3hrs 45 min • 10 sections • 3 each of Math, Writing, and Critical Reading • 1 experimental • Scored differently than most other tests

  3. About the SAT scoring • Multiple Choice • Correct = +1 point • No answer = 0 points • Incorrect = -1/4 point • Grid-Ins • Correct = 1 point • Incorrect = 0 points • The test is made up of 3 sections • Math • Writing • Critical reading • Scoring range is 200-800 per section of the test. • Minimum score is 600 • Maximum score is 2400

  4. To guess or not to guess….. • Since it would take 4 incorrect responses to cancel out 1 correct response it makes sense to guess when you can do so reasonably. • There are 5 answer choices for each question. • Consider you can eliminate until you only have 2 choices…. • Consider you can eliminate until you only have 3 choices…. • Ultimately, you must decide what is in your best interest!

  5. Math Sections • 3 sections, maybe 4 if the experimental is a math • 24 multiple choice (25 minutes) • 8 multiple choice/10 grid ins (25 minutes) • 16 multiple choice (20 minutes) • Four categories • Arithmetic • Basic Algebra • Geometry • Basic Algebra II

  6. Calculator • You may have one, but you don’t have to • One will NOT be provided for you • You may NOT use one with a standard computer keypad • Basically any TI83 or TI 84 (pluses, silver edition, etc.) are ACCEPTABLE • TI 90’s are not okay, neither are Voyagers • TI Inspires should be fine as long as you have the 84 faceplate

  7. Calculator • You have used one in every math class, please take one to the test!!!!!! • Most teachers will let you check one out the Friday before the test, however you must remember to bring it back first thing Monday morning. 

  8. Instructions • Each section of Math on the Sat will begin with the same set of instructions. • The instructions include a few formulas and other information you may need to know to answer some of the questions. • You should learn then instructions before the day of the SAT in order to not wasting valuable time reading/referring to them during the actual test.

  9. Some basic rules you need to remember: • Integers are numbers that are not fractions or decimals • Even numbers are divisible by 2 (if the last digit is divisible by 2 the entire number is) • Odd numbers are not divisible by 2 • The ten digits are: • 0,1,2,3,4,5,6,7,8,9

  10. Factors • Factors are numbers that go into a number evenly. • Example: • The factors of 6 are 1,2,3, and 6 • The number 6 is composite because more than 1 and itself go into it. • The factors of 5 are 1,5 • The number 5 is Prime because its only factors are 1 and 5. • Special things about prime numbers • 0 and 1 are not prime • 2 is the smallest, and only even, prime • Not all odd numbers are prime • The most common use of factors is factoring.

  11. Key Words • Sum is what you get when you add • Difference is what you get when you subtract • Product is what you get when you multiply • Quotient or Ratio is what you get when you divide • Exponents and Powers are the same thing • The number raised to the power is the base • Is means = • More than can mean + or > depending on the problem • Lessthan can mean – or < • At Least means ≥ • No more than means ≤

  12. Order of Operations • The order of operations matters! • Please Excuse My Dear Aunt Sally is okay to remember, but be careful with the part after the excuse. • Parenthesis • Exponents • Multiply OR Divide from left to right • Add OR Subtract from left to right

  13. Fractions • You can only add or subtract when you find common denominators • You multiply by doing numerator x numerator OVER denominator x denominator (top x top over bottom x bottom) • You divide by flipping the denominator (bottom) and multiplying the top by this fraction.

  14. Multiples • Multiples are numbers you get when you multiply a number by another number • Example: • Some multiples of 3 are 3,6,9,12,…. • Some multiples of 5 are 5,10,15,20,… • The most common use of multiples is in finding least common denominators so that you can add or subtract fractions.

  15. Consecutive Integers • Consecutive means one after another • Examples of consecutive integers are: • 1,2,3 • 150,151,152 • x, x+1,x+2 • Consecutive even integers would look like: • 2,4,6 • 10,12,14 • x, x+2, x+4 • Consecutive odd integers would look like: • 3,5,7 • x, x+2, x+4

  16. Exponent Rules • When you multiply bases you add powers • When you divide bases you subtract powers. (Any negative powers need to go across the fraction bar to become positive)

  17. Exponent Rules (2) • When you have a power to a power you multiply • Special Rules • Anything to the zero power is 1.

  18. Factoring • These are the favorite quadratic equations on the SAT, according to “The Princeton Review”

  19. Solving Equations Strategies • Example: • If 4x + 2 = 4, what is the value of 4x – 6? • -6 • -4 • 4 • 8 Options: Actually solve by algebra methods and plug into 4x-6 Solve by graphing and then plug into 4x-6 Make the left side look like the 4x-6 Ans= B

  20. Factoring Example 1 • In the expression k is an integer and k<0. Which of the following is a possible value of k? • -13 • -12 • -6 • 7 • It cannot be determined from the information given • Is there any number you can eliminate? • What are the possible factors of the quadratic? • Foil these out, what are the possible k values? Page 216, correct answer is A

  21. Factoring Example 2 • If 2x – 3y = 5, what is the value of • 5 • 12 • 25 • 100 • Factor the trinomial, think about what one of the factors must be…. Page 217, D

  22. Solving Quadratics- Example 1 • If , which of the following is a possible value for x? • -7 • -1 • 1 • 3 • 7 • The traditional way to solve is to multiply by x and turn into a quadratic. • One possibility is substituting in the answers…. • Another is solving by graphing on the calculator….

  23. Absolute Value For the equations shown above, which of the following is a possible value of x-y? • -14 • -4 • -2 • 1 • 14 • Solve the top equations (could do so graphically) • Try different combinations P220 B

  24. Specific Amounts: Guess and Check Method • Zoe won the raffle at a fair. She will receive the prize money in 5 monthly payments. If each payment is half as much as the previous month’s payment and the total of the payments is $496, what is the amount of the first payment? • $256 • $96 • $84 • $16 • $4 Is there a good place to start with a guess and check method? P222, A

  25. Guess and check #2 • The units digit of a two digit number is 3 times the tens digit. If the digits are reversed the resulting number is 36 more than the original number. What is the original number? • 26 • 36 • 39 • 54 • 93 Page 226, A

  26. Plugging in numbers to guess and check • If Jayme will be J years old in 3 years, then in terms of J, how old was Jayme 5 years ago? • J-8 • J-5 • J-3 • J+5 • J+8 Pick any number you want for J. I suggest something larger than 3+5 which is 8; so maybe 10? Page 227, A

  27. Plugging in continued • The sum of four consecutive positive even integers is x. In terms of x, what is the sum of the second and third integers? • (x-12)/4 • (x-6)/2 • 2x+6 • x/2 • (x^2 – 3x)/4 P228, D

  28. One more plug in • If a-b is a multiple of 7, which of the following must also be a multiple of 7? • ab • a + b • (a + b)/2 • (b - a)/2 • b - a p232E

  29. Strange operations…. • If x#y = 1/(x-y), what is the value of ½ # 1/3 • 6 • 6/5 • 1/6 • -1 • -6 Page 240, A

  30. Percentages • Remember that % means “out of 100” • So 30% is 30/100 • If you want to find a percent of a number you multiply by the decimal version of the % or the percent/100. • For example 20% of 80 is (.20)(80)=16 or (20/100)(80) = 16 • If you want to do some “Plug-ins” to test 100 is a great number because it is so easy to find the %. For example: 15% of 100 is 15. 

  31. Percent Change • Percent change = Difference/original x 100% • The price of a shirt was raised from $12 to $18. What is the percent of change? • (18-12)/12 x100% = 6/12 x 100% = 50%

  32. Try a percent problem • A number is increased by 25% and then decreased by 20%. The result is what percent of the original number? • 80 • 100 • 105 • 120 • 125 P257 B

  33. Probability and Odds • Probability is basically correct/total • What is the probability of rolling a 1 on a dice? • There is one 1 and 6 sides, so 1/6 • Odds are correct/incorrect • What are the odds you will roll a 1 on a dice? • There is one 1 and five non-1s on a dice, so 1/5

  34. Probability Example • A bag contains 7 blue marbles and 14 marbles that are not blue. If one marble is drawn at random from the bag, what is the probability that the marble is blue? • 1/7 • 1/3 • ½ • 2/3 • 3/7 • So how many are “correct”? • How many marbles total? P267 B

  35. Another Probability • A jar contains only red marbles and white marbles. If the probability of selecting a red marble is r/y, which of the following expressions gives the probability of selecting a white marble in terms of r and y? • (r-y)/y • (y-r)/y • y/(y-r) • r/y • y/r So, what strategy? B

  36. Permutations • Hal wrote 7 essays in his English class. He wants to put all 7 essays in his portfolio and is deciding in what order to place the essays. In how many different orders can Hal arrange his essays? • 49 • 420 • 5040 • 5670 • 10549 • Options: • Tree diagrams • blanks C

  37. Geometry- Triangles • A triangle contains 180⁰ • Equilateral triangles have all 3 angles the same • Isosceles triangles have two angles that are equal • A right triangle has a 90⁰ angle • The area of a triangle is 1/2bh • The perimeter of a triangle is the sum of the 3 sides • If a right triangle then a2 + b2 = c2

  38. Geometry- Circles, Squares, and Rectangles • A circle contains 360⁰ • r = radius, d = diameter • Area = πr2 • Perimeter = 2πr = πd • Squares contain 360⁰ (with each corner being 90⁰) and all sides are equal • Perimeter = 4s, where s=length of a side • Area = s2 • Rectangles contain 360⁰ (with each corner being 90⁰) and have pairs of sides that have equal lengths • Perimeter = 2(length) + 2(width) • Area = (length)(width)

  39. Basic Triangle Example • If the area of ∆ABC in the figure below is 30. What is the length of DC? • 2 • 4 • 6 • 8 • 12 A 5 C B 4 D P298 D

  40. One More Triangle • In the figure below, what is the value of x+y+z? • 90 • 180 • 270 • 360 • 450 y x z P304 D

  41. Grid Ins • NO DEDUCTIONS FOR WRONG ANSWERS! • If you can come up with an answer; go for it! • A wrong answer is no worse than a blank answer. • Start putting answers in from left. • No mixed numbers! • Use improper fractions or decimals. • Do not do 3 ½ , you need to put 7/2 or 3.5 • You do not need to reduce fractions. • These are usually easier because the answers cannot have variables in them. 

  42. In Conclusion • In each section the problems get progressively more difficult. • Make sure your read through practice materials and become familiar with directions and formulas that are given. Do this so you do not have to spend valuable time during the test figuring things out. • Take practice tests (be sure to time yourself) before the test to get a feel for how fast you need to work. • Best wishes in your testing endeavors!!!! 

  43. Internet Resources • http://sat.collegeboard.org/home • http://www.majortests.com/sat/problem-solving.php • http://www.testprepreview.com/sat_practice.htm

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